The first things we learn about Prince Fabrizio are that he's proud and he's huge enough to intimidate anyone who looks the wrong way at him. At first, it's actually tough to figure out whether this guy is going to be our hero or our villain. He sounds super intimidating, to be honest:
[The] Prince had risen to his feet; the sudden movement of his huge frame made the floor tremble, and a glint of pride flashed in his light blue eyes at this fleeting confirmation of his lordship over both human beings and their works. (1.7)
Centuries of royal blood have convinced the Prince that he practically rules the world like a god. If his royal status isn't enough to make him feel that way, his giant body sure is. And at this point, we're left wondering, "So why should we like this guy?"
In the early pages of this book, Lampedusa is almost obsessed with describing how imposing the Prince's is:
Not that he was fat; just very large and very strong; in houses inhabited by common mortals his head would touch the lowest rosette on the chandeliers; his fingers could twist a ducat coin as it if were mere paper. (1.9)
The guy sounds like a royal monster who could eat children if he wanted to, but the truth is that his short temper is evened out by his love for his family and his delicate manners. So Fabrizio isn't a raging lion, he's more like an agile, graceful leopard—the official symbol of the Prince's family, zing!
Prince Fabrizio has bigger problems than not being a royal anymore (and having to listen to Lorde all day). A lifetime of idleness has left him feeling like there's no real point to what he does. Plus he's pretty bummed out about getting older. The two main problems in his life—his age and the end of the Sicilian aristocracy—are totally unavoidable. And even if the guy had the power to save his royal status, he wouldn't feel any motivation to do it.
As the narrator tells us,
Between the pride and intellectuality of his mother and the sensuality and irresponsibility of his father, poor Prince Fabrizio lived in perpetual discontent under his Jovelike frown, watching the ruin of his own class and his own inheritance without ever making, still less wanting to make, any move toward saving it. (1.12)
In other words, Prince Fabrizio knows that there's no good reason to defend an entire class of people who are rich and powerful just because they were born into a certain family. He knows that the future belongs to people who've worked hard for what they have.
In his darkest moments, Prince Fabrizio feels dislike for the one person in this book he loves most—his nephew Tancredi: "For the first time he felt a touch of rancor prick him at sight of Tancredi; this fop with the pinch-in waist under his dark blue suit had been the cause of those sour thoughts of his about death two hours ago" (2.55). After all, Tancredi is young, handsome, and charming while Fabrizio is old, bitter, and kind of depressing.
A lifetime of doing nothing hasn't just made Fabrizio bored; it's also made him super philosophical about the both his death and the death of his entire social class. Early in the novel, he knows that his day will eventually come, just like it has for the Sicilian aristocracy. He thinks back on all the stuff in his life and realizes,
Don Calogero's tailcoat, Concetta's love, Tancredi's blatant infatuation, his own cowardice; even the threatening beauty of that girl Angelica: bad things, rubble preceding an avalanche. (2.84)
All he can see around him is destruction that's totally unpreventable.
It's all just part of the natural process of new generations sweeping old ones into the trash bin of history. The only thing that ever seems to cheer the Prince up is the thought of being romantically involved with young, beautiful women. But he can only keep this fantasy going for so long.
By the end of the novel, Fabrizio has already started to think of himself as a dead old mummy that can be hung from a wall. But on the bright side, he feels like he'd make a good mummy:
[He'd] look magnificent on that wall, tall and big as he was, terrifying girls by the set smile on his sandpaper face, by his long, long white piqué trousers. (6.40)
He likes the thought that something of him can be preserved after he dies. But like his dog Bendicò, he knows that even the mummified version of him will turn to dust. So in the end, it's tough to say what conclusion he's reached other than, "Everybody dies."